Question

Triangle A and Triangle B have the same base. The height of Triangle B ice the height of Triangle A. How many times greater is the area of is tw Triangle B? Big Ideas Math G

Answer 1

The area of Triangle B is twice the area of Triangle A .

Explanation:

Given as :

Triangle A and Triangle B have same base

The height of Triangle A twice Triangle B

For Triangle A

The base of Triangle A =
`b_1` = b

The height of Triangle A =
`h_1` = h

Let The area of Triangle A =
`A_1`

∵ The Area of Triangle =
`(1)/(2)` × base × height

So,
`A_1` =
`(1)/(2)` × b × h ......1

For Triangle B

The base of Triangle B =
`b_2` = b

The height of Triangle B =
`h_2` = twice the height of Triangle A

I.e
`h_2` = 2 h

Let The area of Triangle B =
`A_2`

So,
`A_2` =
`(1)/(2)` × b × 2 h ........2

Now, Comparing both equation 1 and 2

∵
`A_2` =
`(1)/(2)` × b × 2 h

Or,
`A_2` = 2 ×
`(1)/(2)` × b × h

Or,
`A_2` = 2 ×
`A_1`

So, The area of Triangle B = 2 times The area of Triangle A

Hence, The area of Triangle B is twice the area of Triangle A . Answer